The Sims 2: Nightlife on Xbox 360?

No. The Sims 2: Nightlife (Expansion Pack) was PC/Mac only (March 2005).

The Sims on Xbox 360

• The Sims 3 (Oct 2010) — Only Sims title on Xbox 360. Includes base + some EP content (Ambitions, Late Night objects). No Nightlife EP.
• The Sims 2 (Console) — Released on PS2, GameCube, Xbox (Original), PSP, DS. Not Xbox 360.

If You Want Nightlife Content

• PC (Steam/EA App): The Sims 2: Ultimate Collection (often free for legacy owners) includes Nightlife + all EPs/SPs.
• Original Xbox (Backward Compat on 360): The Sims 2 (base) + The Sims 2: Pets are BC on Xbox 360. Nightlife not released on Xbox.